A characterization of affine hyperquadrics

In this paper, using the existence of special exhaustions that satisfy the complex homogeneous Monge–Ampère equation and curvature properties are given characterizations of the affine hyperquadric and other special Stein manifolds. Mathematics Subject Classification (2000) 32W20, 32V40     

A variational problem with lack of compactness for H(S;S) maps of prescribed degree

We consider, for maps in H^1/2(S¹;S¹), a family of (semi)norms equivalent to the standard one. We ask whether, for such a norm, there is some map in H^1/2(S¹;S¹) of prescribed topological degree equal to 1 and minimal norm. In general, the answer is no, due to concentration phenomena. The existence of a minimal map is sensitive to small perturbations of the norm. We derive a sufficient condition for the existence of minimal maps. In particular, we prove that, for every given norm, there are arbitrarily small perturbations of it for which the minimum is attained. In case there is no minimizer, we determine the asymptotic behavior of minimizing sequences. We prove that, for such minimizing sequences, the energy concentrates near a point of S¹. We describe this concentration in terms of bubbling-off of circles.     

Characters of Fundamental Representations of Quantum Affine Algebras

We give closed formulae for the q-characters of the fundamental representations of the quantum loop algebra of a classical Lie algebra, in terms of a family of partitions satisfying some simple properties. We also give the multiplicities of the eigenvalues of the imaginary subalgebra in terms of these partitions.     

Magnetic and electrokinetic manipulations on a microchip device for bead-based immunosensing applications

The combination of electrophoretic and magnetic manipulations with electrochemical detection for a versatile microfluidic and bead-based biosensing application is demonstrated. Amperometric detection is performed in an off-channel setup by means of a voltammetric cell built at the microchannel outlet and using a gold working electrode. Superparamagnetic particles are introduced and handled inside the channel by means of an external permanent magnet in combination with the electrogenerated flow which allows reproducible loading. The specific detection of phenol as electroactive alkaline phosphatase product is used in this study as proof of concept for a sensitive protein quantification. Characterizations and optimization of different parameters have been carried out in order to achieve the best detection signal. The applicability of the device has been finally demonstrated by the detection of rabbit IgG as model protein after an immunoassay performed on magnetic particles as immobilization platform. A comparison between the electrochemical detection using the developed device and the optical standard detection revealed similar performances with, however, extremely lower amount of reagent used and shorter analysis time. The developed electrophoretic- and magnetic-based chip may open the way to several other biosensing applications with interest not only for other proteins but also for DNA analysis, cell counting, and environmental control.     

Synthesis and coordination properties of new macrocyclic ligands: equilibrium studies and crystal structures

The synthesis and characterization of two new macrocyclic ligands, the bis-macrocyclic compound 2,6-bis(1,4,13-triaza-7,10-dioxacyclopentadec-1-ylmethyl)phenol (L) and 38-methoxy-1,4,13,16,19,28-hexaaza-7,10,22,25-tetraoxatricyclo[14.14.7.1(32,36)]octatriconta-32,34,Delta(36,38)-triene (L1) are reported. Equilibrium studies of basicity and coordination properties toward metal ions such as Cu(II), Zn(II), Cd(II) and Pb(II) were performed for ligand by potentiometric measurements in aqueous solution (298.1 +/- 0.1 K, I= 0.15 mol dm(-3)). L behaves as a hexaprotic base (logK(1)= 10.93, logK(2)= 9.70, logK(3)= 8.79, logK(4)= 8.05, logK(5)= 6.83, logK(6)= 2.55). All metal ions form stable mono- and dinuclear complexes: logK(MLH(-1))= 25.61 for Cu(II), 15.37 for Zn(II), 12.58 for Cd(II) and 13.79 for Pb(II); logK(M(2)LH(-1))= 31.61 for Cu(II), 23.38 for Zn(II), 24.49 for Cd(II) and 23.68 for Pb(II). All these dinuclear species show a great tendency to add the OH(-) group: the equilibrium constant for the addition reaction was found to be logK(M(2)LH(-1)OH)= 4.77 for Cu(II), 5.66 for Zn(II), 2.8 for Cd(II) and 3.18 for Pb(II). In the case of Ni(II), kinetic inertness prevents the possibility of solution studies. The dinuclear solid adducts [Ni(2)H(-1)L(N(3))(3)].EtOH and [Cu(2)H(-1)L(N(3))](ClO(4))(2) were characterized by X-ray analysis.     

Cu+(H2) and Na+(H2) adducts in exchanged ZSM-5 zeolites

Cu(I) ions in Cu-ZSM-5 form Cu+(H2) complexes, stable at room temperature and sub-atmospheric H2 pressure, which do not have any homogeneous analogue except for matrix-isolated [Cu(eta2-H2)Cl]. Comparison with the unstable Na+(H2) adducts formed in the parent Na-ZSM-5 zeolite allow the conclusion that the Cu(I)/H2 bond is governed by sigma-pi overlap forces.